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<h1><img src="../../../../boost.png" alt="boost.png (6897 bytes)" align=
"middle" width="277" height="86">Boost.MultiIndex Ranked indices reference</h1>

<div class="prev_link"><a href="ord_indices.html"><img src="../prev.gif" alt="ordered_indices" border="0"><br>
Ordered indices
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Boost.MultiIndex reference
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Hashed indices
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<hr>

<h2>Contents</h2>

<ul>
  <li><a href="#rnk_index_fwd_synopsis">Header
    <code>"boost/multi_index/ranked_index_fwd.hpp"</code> synopsis</a></li>
  <li><a href="#synopsis">Header
    <code>"boost/multi_index/ranked_index.hpp"</code> synopsis</a>
    <ul>
      <li><a href="#unique_non_unique">
        Index specifiers <code>ranked_unique</code> and <code>ranked_non_unique</code>
        </a></li>
      <li><a href="#rnk_indices">Ranked indices</a>
        <ul>
          <li><a href="#complexity_signature">Complexity signature</a></li>
          <li><a href="#instantiation_types">Instantiation types</a></li>
          <li><a href="#types">Nested types</a></li>
          <li><a href="#set_operations">Set operations</a></li>
          <li><a href="#rank_operations">Rank operations</a></li>
          <li><a href="#serialization">Serialization</a></li>
        </ul>
      </li>
    </ul>
  </li>
</ul>

<h2>
<a name="rnk_index_fwd_synopsis">Header
<a href="../../../../boost/multi_index/ranked_index_fwd.hpp">
<code>"boost/multi_index/ranked_index_fwd.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=comment>// index specifiers ranked_unique and ranked_non_unique</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>consult ranked_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ranked_unique</span><span class=special>;</span>
<span class=keyword>template</span><span class=special>&lt;</span><b>consult ranked_non_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ranked_non_unique</span><span class=special>;</span>

<span class=comment>// indices</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span> <span class=keyword>class</span> <b>index name is implementation defined</b><span class=special>;</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<p>
<code>ranked_index_fwd.hpp</code> provides forward declarations for index specifiers 
<a href="#unique_non_unique"><code>ranked_unique</code> and <code>ranked_non_unique</code></a> and
their associated <a href="#rnk_indices">ranked index</a> classes.
</p>

<h2>
<a name="synopsis">Header
<a href="../../../../boost/multi_index/ranked_index.hpp">
<code>"boost/multi_index/ranked_index.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>initializer_list</span><span class=special>&gt;</span>

<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=comment>// index specifiers ranked_unique and ranked_non_unique</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>consult ranked_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ranked_unique</span><span class=special>;</span>
<span class=keyword>template</span><span class=special>&lt;</span><b>consult ranked_non_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>ranked_non_unique</span><span class=special>;</span>

<span class=comment>// indices</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span> <span class=keyword>class</span> <b>index class name implementation defined</b><span class=special>;</span>

<span class=comment>// index comparison:</span>

<span class=comment>// <b>OP</b> is any of ==,&lt;,!=,&gt;,&gt;=,&lt;=</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=comment>// index specialized algorithms:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h3><a name="unique_non_unique">
Index specifiers <code>ranked_unique</code> and <code>ranked_non_unique</code>
</a></h3>

<p>
These <a href="indices.html#index_specification">index specifiers</a> allow
for insertion of <a href="#rnk_indices">ranked indices</a> without and with
allowance of duplicate elements, respectively. The syntax of <code>ranked_unique</code>
and <code>ranked_non_unique</code> coincide, thus we describe them in a grouped manner.
<code>ranked_unique</code> and <code>ranked_non_unique</code> can be instantiated in
two different forms, according to whether a tag list for the index is provided or not:
</p>

<blockquote><pre>
<span class=keyword>template</span><span class=special>&lt;</span>
  <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>Compare</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>less</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;</span>
<span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=special>(</span><span class=identifier>ranked_unique</span> <span class=special>|</span> <span class=identifier>ranked_non_unique</span><span class=special>)</span><span class=special>;</span>

<span class=keyword>template</span><span class=special>&lt;</span>
  <span class=keyword>typename</span> <span class=identifier>TagList</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>Compare</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>less</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;</span>
<span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=special>(</span><span class=identifier>ranked_unique</span> <span class=special>|</span> <span class=identifier>ranked_non_unique</span><span class=special>)</span><span class=special>;</span>
</pre></blockquote>

<p>
If provided, <code>TagList</code> must be an instantiation of the class template
<a href="indices.html#tag"><code>tag</code></a>.
The template arguments are used by the corresponding index implementation,
refer to the <a href="#rnk_indices">ranked indices</a> reference section for further
explanations on their acceptable type values.
</p>

<h3><a name="rnk_indices">Ranked indices</a></h3>

<p>
Ranked indices are a variation of <a href="ord_indices.html">ordered indices</a>
providing additional capabilities for calculation of and access by rank; the <i>rank</i> of an element is the
distance to it from the beginning of the index. Besides this extension, ranked indices replicate the
public interface of ordered indices with the difference, complexity-wise, that 
<a href="#complexity_signature">hinted insertion</a> and <a href="#complexity_signature">deletion</a>
are done in logarithmic rather than constant time. Also, execution times and memory consumption are
expected to be poorer due to the internal bookkeeping needed to maintain rank-related information
(an exception being <a href="#count"><code>count</code> operations</a>, which are actually faster).
As with ordered indices, ranked indices can be unique (no duplicate elements are allowed)
or non-unique: either version is associated to a different index specifier, but
the interface of both index types is the same.
</p>

<p>
In what follows, we only describe the extra operations provided by ranked indices or those
operations with improved performance: for the
rest refer to the <a href="ord_indices.html#ord_indices">documentation</a> for ordered
indices, bearing in mind the occasional differences in complexity.
</p>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<b>implementation defined </b><span class=identifier>unbounded</span><span class=special>;</span> <span class=comment>// see range_rank()</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined: dependent on types Value, Allocator,
  TagList, KeyFromValue, Compare</b><span class=special>&gt;</span>
<span class=keyword>class</span> <b>name is implementation defined</b>
<span class=special>{</span> 
<span class=keyword>public</span><span class=special>:</span>
  <span class=comment>// types:</span>

  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span>         <span class=identifier>key_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Value</span>                                      <span class=identifier>value_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>KeyFromValue</span>                               <span class=identifier>key_from_value</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Compare</span>                                    <span class=identifier>key_compare</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>value_compare</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>key_from_value</span><span class=special>,</span><span class=identifier>key_compare</span><span class=special>&gt;</span>   <span class=identifier>ctor_args</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>TagList</span>                                    <span class=identifier>tag_list</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Allocator</span>                                  <span class=identifier>allocator_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>reference</span>              <span class=identifier>reference</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>const_reference</span>        <span class=identifier>const_reference</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>const_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>size_type</span><span class=special>;</span>      
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>difference_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>pointer</span>                <span class=identifier>pointer</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>const_pointer</span>          <span class=identifier>const_pointer</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>equivalent to
    std::reverse_iterator&lt;iterator&gt;</b>                  <span class=identifier>reverse_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>equivalent to
    std::reverse_iterator&lt;const_iterator&gt;</b>            <span class=identifier>const_reverse_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>same as owning container                   </b><span class=identifier>node_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>following [container.insert.return] spec   </b><span class=identifier>insert_return_type</span><span class=special>;</span>

  <span class=comment>// construct/copy/destroy:</span>

  <b>index class name</b><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>=(</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <b>index class name</b><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>=(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>initializer_list</span><span class=special>&lt;</span><span class=identifier>value_type</span><span class=special>&gt;</span> <span class=identifier>list</span><span class=special>);</span>

  <span class=identifier>allocator_type</span> <span class=identifier>get_allocator</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>

  <span class=comment>// iterators:</span>

  <span class=identifier>iterator</span>               <span class=identifier>begin</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>begin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>iterator</span>               <span class=identifier>end</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>end</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>reverse_iterator</span>       <span class=identifier>rbegin</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>rbegin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>reverse_iterator</span>       <span class=identifier>rend</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>rend</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>cbegin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span>         <span class=identifier>cend</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>crbegin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_reverse_iterator</span> <span class=identifier>crend</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
 
  <span class=identifier>iterator</span>       <span class=identifier>iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>const_iterator</span> <span class=identifier>iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// capacity:</span>

  <span class=keyword>bool</span>      <span class=identifier>empty</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>size</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>max_size</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>

  <span class=comment>// modifiers:</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span><span class=special>...</span> <span class=identifier>Args</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>emplace</span><span class=special>(</span><span class=identifier>Args</span><span class=special>&amp;&amp;...</span> <span class=identifier>args</span><span class=special>);</span>
  <span class=keyword>template</span> <span class=special>&lt;</span><span class=keyword>typename</span><span class=special>...</span> <span class=identifier>Args</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>emplace_hint</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Args</span><span class=special>&amp;&amp;...</span> <span class=identifier>args</span><span class=special>);</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>insert</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>InputIterator</span><span class=special>&gt;</span>
  <span class=keyword>void</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>InputIterator</span> <span class=identifier>first</span><span class=special>,</span><span class=identifier>InputIterator</span> <span class=identifier>last</span><span class=special>);</span>
  <span class=keyword>void</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>initializer_list</span><span class=special>&lt;</span><span class=identifier>value_type</span><span class=special>&gt;</span> <span class=identifier>list</span><span class=special>);</span>
  <span class=identifier>insert_return_type</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>node_type</span><span class=special>&amp;&amp;</span> <span class=identifier>nh</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>const_iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>node_type</span><span class=special>&amp;&amp;</span> <span class=identifier>nh</span><span class=special>);</span>

  <span class=identifier>node_type</span> <span class=identifier>extract</span><span class=special>(</span><span class=identifier>const_iterator</span> <span class=identifier>position</span><span class=special>);</span>
  <span class=identifier>node_type</span> <span class=identifier>extract</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>

  <span class=identifier>iterator</span>  <span class=identifier>erase</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>);</span>
  <span class=identifier>size_type</span> <span class=identifier>erase</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span>  <span class=identifier>erase</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>first</span><span class=special>,</span><span class=identifier>iterator</span> <span class=identifier>last</span><span class=special>);</span>

  <span class=keyword>bool</span> <span class=identifier>replace</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>bool</span> <span class=identifier>replace</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>&gt;</span> <span class=keyword>bool</span> <span class=identifier>modify</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Rollback</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>modify</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>,</span><span class=identifier>Rollback</span> <span class=identifier>back</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>&gt;</span> <span class=keyword>bool</span> <span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Rollback</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>,</span><span class=identifier>Rollback</span> <span class=identifier>back</span><span class=special>);</span>
  
  <span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>void</span> <span class=identifier>clear</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Index</span><span class=special>&gt;</span> <span class=keyword>void</span> <span class=identifier>merge</span><span class=special>(</span><span class=identifier>Index</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Index</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>merge</span><span class=special>(</span>
    <span class=identifier>Index</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>remove_reference_t</span><span class=special>&lt;</span><span class=identifier>Index</span><span class=special>&gt;::</span><span class=identifier>const_iterator</span> <span class=identifier>i</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Index</span><span class=special>&gt;</span>
  <span class=keyword>void</span> <span class=identifier>merge</span><span class=special>(</span>
    <span class=identifier>Index</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
    <span class=keyword>typename</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>remove_reference_t</span><span class=special>&lt;</span><span class=identifier>Index</span><span class=special>&gt;::</span><span class=identifier>const_iterator</span> <span class=identifier>first</span><span class=special>,</span>
    <span class=keyword>typename</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>remove_reference_t</span><span class=special>&lt;</span><span class=identifier>Index</span><span class=special>&gt;::</span><span class=identifier>const_iterator</span> <span class=identifier>last</span><span class=special>);</span>
      
  <span class=comment>// observers:</span>

  <span class=identifier>key_from_value</span> <span class=identifier>key_extractor</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>key_compare</span>    <span class=identifier>key_comp</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>value_compare</span>  <span class=identifier>value_comp</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// set operations:</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>find</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>find</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>count</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>count</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>contains</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>contains</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>lower_bound</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>lower_bound</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>upper_bound</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>upper_bound</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>equal_range</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>equal_range</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// range:</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>LowerBounder</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>UpperBounder</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>range</span><span class=special>(</span>
    <span class=identifier>LowerBounder</span> <span class=identifier>lower</span><span class=special>,</span><span class=identifier>UpperBounder</span> <span class=identifier>upper</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// rank operations:</span>

  <span class=identifier>iterator</span>  <span class=identifier>nth</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>rank</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>find_rank</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>find_rank</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>lower_bound_rank</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>lower_bound_rank</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>upper_bound_rank</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>upper_bound_rank</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>size_type</span><span class=special>,</span><span class=identifier>size_type</span><span class=special>&gt;</span> <span class=identifier>equal_range_rank</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleCompare</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>size_type</span><span class=special>,</span><span class=identifier>size_type</span><span class=special>&gt;</span> <span class=identifier>equal_range_rank</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatibleCompare</span><span class=special>&amp;</span> <span class=identifier>comp</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>LowerBounder</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>UpperBounder</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>size_type</span><span class=special>,</span><span class=identifier>size_type</span><span class=special>&gt;</span>
  <span class=identifier>range_rank</span><span class=special>(</span><span class=identifier>LowerBounder</span> <span class=identifier>lower</span><span class=special>,</span><span class=identifier>UpperBounder</span> <span class=identifier>upper</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
<span class=special>};</span>

<span class=comment>// index comparison:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>==(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=identifier>x</span><span class=special>.</span><span class=identifier>size</span><span class=special>()==</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>size</span><span class=special>()&amp;&amp;</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>equal</span><span class=special>(</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>begin</span><span class=special>());</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>lexicographical_compare</span><span class=special>(</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>end</span><span class=special>(),</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>y</span><span class=special>.</span><span class=identifier>end</span><span class=special>());</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>!=(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=special>!(</span><span class=identifier>x</span><span class=special>==</span><span class=identifier>y</span><span class=special>);</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&gt;(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=identifier>y</span><span class=special>&lt;</span><span class=identifier>x</span><span class=special>;</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&gt;=(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=special>!(</span><span class=identifier>x</span><span class=special>&lt;</span><span class=identifier>y</span><span class=special>);</span>
<span class=special>}</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>arg set 1</b><span class=special>,</span><b>arg set 2</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>&lt;=(</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 1</b><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
  <span class=keyword>const</span> <b>index class name</b><span class=special>&lt;</span><b>arg set 2</b><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=special>!(</span><span class=identifier>x</span><span class=special>&gt;</span><span class=identifier>y</span><span class=special>);</span>
<span class=special>}</span>

<span class=comment>// index specialized algorithms:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h4><a name="complexity_signature">Complexity signature</a></h4>

<p>
We follow the terminology described in the 
<a href="indices.html#complexity_signature">complexity signature
section</a>. The complexity signature of ranked indices is:
<ul>
  <li>copying: <code>c(n)=n*log(n)</code>,</li>
  <li>insertion: <code>i(n)=log(n)</code>,</li>
  <li>hinted insertion: <b><code>h(n)=log(n)</code></b>,</li>
  <li>deletion: <b><code>d(n)=log(n)</code></b> ,</li>
  <li>replacement: <code>r(n)=1</code> (constant) if the element position does not
    change, <code>r(n)=log(n)</code> otherwise,</li>
  <li>modifying: <code>m(n)=1</code> (constant) if the element position does not
    change, <code>m(n)=log(n)</code> otherwise.</li>
</ul>
</p>
<p>
These complexity guarantees are the same as those of
<a href="ord_indices.html#complexity_signature">ordered indices</a>
except for hinted insertion and deletion, which are <code>log(n)</code> here and amortized constant there.
</p>

<h4><a name="instantiation_types">Instantiation types</a></h4>

<p>Ranked indices are instantiated internally to <code>multi_index_container</code> and
specified by means of <a href="indices.html#indexed_by"><code>indexed_by</code></a>
with <a href="#unique_non_unique"> index specifiers <code>ranked_unique</code>
and <code>ranked_non_unique</code></a>. Instantiations are dependent on the
following types:
<ul>
  <li><code>Value</code> from <code>multi_index_container</code>,</li>
  <li><code>Allocator</code> from <code>multi_index_container</code>,</li>
  <li><code>TagList</code> from the index specifier (if provided, otherwise <code>tag&lt;&gt;</code> is assumed),</li>
  <li><code>KeyFromValue</code> from the index specifier,</li>
  <li><code>Compare</code> from the index specifier.</li>
</ul>
These types are subject to the same requirements as specified for
<a href="ord_indices.html#instantiation_types">ordered indices</a>.
</p>

<h4><a name="types">Nested types</a></h4>

<code>iterator<br>
const_iterator</code>

<blockquote>
These types depend only on <code>node_type</code> and the position of
the index in the <code>multi_index_container</code>.
</blockquote>

<h4><a name="set_operations">Set operations</a></h4>

<p>
See the documentation of ordered indices for an explanation of the notions of
<a href="ord_indices.html#set_operations"><i>compatible extension</i> and 
<i>compatible key</i></a>, which are referred to below.
</p>

<a name="count">
<code>template&lt;typename CompatibleKey><br>
size_type count(const CompatibleKey&amp; x)const;
</code></a>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
size_type count(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<h4><a name="rank_operations">Rank operations</a></h4>

<p>
The <i>rank</i> of an iterator <code>it</code> of a given container <code>c</code> (and,
by extension, of the element it points to if the iterator is dereferenceable)
is <code>std::distance(c.begin(),it)</code>.
</p>

<p>
See the documentation of ordered indices for an explanation of the notions of
<a href="ord_indices.html#set_operations"><i>compatible extension</i>, 
<i>compatible key</i></a>, 
<a href="ord_indices.html#range_operations"><i>lower bounder</i> and <i>upper bounder</i></a>, which are
referred to below.
</p>

<code>iterator nth(size_type n)const;</code>

<blockquote>
<b>Effects:</b> Returns an iterator with rank <code>n</code>,
or <code>end()</code> if <code>n&gt;=size()</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>size_type rank(iterator position)const;
</code>

<blockquote>
<b>Requires:</b> <code>position</code> is a valid iterator of the index.<br>
<b>Effects:</b> Returns the rank of <code>position</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey> size_type find_rank(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>rank(find(k))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
size_type find_rank(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>rank(find(x,comp))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
size_type lower_bound_rank(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>rank(lower_bound(x))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
size_type lower_bound_rank(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>rank(lower_bound(x,comp))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
size_type upper_bound_rank(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>rank(upper_bound(x))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
size_type upper_bound_rank(const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>rank(upper_bound(x,comp))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
std::pair&lt;size_type,size_type> equal_range_rank(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
<code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to <code>make_pair(lower_bound_rank(x),upper_bound_rank(x))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey,typename CompatibleCompare><br>
std::pair&lt;size_type,size_type> equal_range_rank(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x,const CompatibleCompare&amp; comp)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleCompare</code>)
is a compatible extension of <code>key_compare</code>.<br>
<b>Effects:</b> Equivalent to
<code>make_pair(lower_bound_rank(x,comp),upper_bound_rank(x,comp))</code>.<br>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
</blockquote>

<code>template&lt;typename LowerBounder,typename UpperBounder><br>
std::pair&lt;size_type,size_type> range_rank(<br>
&nbsp;&nbsp;LowerBounder lower,UpperBounder upper)const;
</code>

<blockquote>
<b>Requires:</b> <code>LowerBounder</code> and <code>UpperBounder</code> are
a lower and upper bounder of <code>key_compare</code>, respectively.<br>
<b>Effects:</b> Equivalent to 
<blockquote><pre>
<span class=keyword>auto</span> <span class=identifier>p</span><span class=special>=</span><span class=identifier>range</span><span class=special>(</span><span class=identifier>lower</span><span class=special>,</span><span class=identifier>upper</span><span class=special>);</span>
<span class=keyword>return</span> <span class=identifier>make_pair</span><span class=special>(</span><span class=identifier>rank</span><span class=special>(</span><span class=identifier>p</span><span class=special>.</span><span class=identifier>first</span><span class=special>),</span><span class=identifier>rank</span><span class=special>(</span><span class=identifier>p</span><span class=special>.</span><span class=identifier>second</span><span class=special>));</span>
</pre></blockquote>
<b>Complexity:</b> <code>O(log(n))</code>.<br>
<b>Variants:</b> In place of <code>lower</code> or <code>upper</code> (or both),
the singular value <code>boost::multi_index::unbounded</code> can be
provided. This acts as a predicate which all values of type <code>key_type</code>
satisfy.<br>
</blockquote>

<h4><a name="serialization">Serialization</a></h4>

<p>
The prerequisites and postconditions associated to serialization of
<code>multi_index_container</code>s with ranked indices are exactly the same
as those of <a href="ord_indices.html#serialization">ordered indices</a>.

<hr>

<div class="prev_link"><a href="ord_indices.html"><img src="../prev.gif" alt="ordered_indices" border="0"><br>
Ordered indices
</a></div>
<div class="up_link"><a href="index.html"><img src="../up.gif" alt="Boost.MultiIndex reference" border="0"><br>
Boost.MultiIndex reference
</a></div>
<div class="next_link"><a href="hash_indices.html"><img src="../next.gif" alt="hashed indices" border="0"><br>
Hashed indices
</a></div><br clear="all" style="clear: all;">

<br>

<p>Revised February 5th 2022</p>

<p>&copy; Copyright 2003-2022 Joaqu&iacute;n M L&oacute;pez Mu&ntilde;oz.
Distributed under the Boost Software 
License, Version 1.0. (See accompanying file <a href="../../../../LICENSE_1_0.txt">
LICENSE_1_0.txt</a> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

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